Abstract: We show that for every $m \in {\mathbb N}$, there exists an $n\in {\mathbb N}$ such that every embedding of the complete graph $K_{n}$ in ${\mathbb R}^{3}$ contains a link of two components whose linking number is at least $m$. Furthermore, there exists an $r \in {\mathbb N}$ such that every embedding of $K_{r}$ in ${\mathbb R}^{3}$ contains a knot $Q$ with $ \vert a_{2}(Q) \vert \geq m$, where $a_{2}(Q)$ denotes the second coefficient of the Conway polynomial of $Q$.